Đáp án:
Giải thích các bước giải:
* (2x+1)²=25 * $5^{x+2}$ =625
⇒ (2x+1)²=(±5)² ⇒$5^{x+2}$ = $5^{4}$
⇒2x+1=±5 ⇒ x+2=4
⇒ 2x ∈ {4,-6} ⇒x=2
⇒ x ∈ {2,-3}
*(2x-3)²=36
⇒(2x-3)²=(±6)²
⇒ 2x ∈ {9,-3}
⇒x ∈ {$\frac{9}{2}$, $\frac{x-3}{2}$}
* (2x-1)³=-8
⇒ (2x-1)³=(-2)³
⇒2x-1=-2
⇒2x=-1
⇒x=$\frac{-1}{2}$
* $(x-1)^{x+2}$ = $(x-1)^{x+6}$
⇒$(x-1)^{x+2}$ -$(x-1)^{x+6}$ =0
⇒ $(x-1)^{x+2}$ × (1-$(x-1)^{4}$)
⇒(\(\left[ \begin{array}{l}(x-1)^{x+2}=0\\1-(x-1)^{4}=0\end{array} \right.\) )
⇒(\(\left[ \begin{array}{l}x-1=0\\(x-1)^{4}=1\end{array} \right.\) )
⇒\(\left[ \begin{array}{l}x=1\\x-1=±1\end{array} \right.\)
* x²+x=0
⇒x(x+1)=0
⇒\(\left[ \begin{array}{l}x=0\\x+1=0\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=0\\x=-1\end{array} \right.\)
Chúc bạn học tốt !
